CoUrSe ModUle SUMMary and UnpaCkIng of StandardS | 93Lesson 25: Geometric Sequences and Exponential Growth and Decay
● (^) Students use geometric sequences to model situations of exponential growth and
decay.
● (^) Students write geometric sequences explicitly and recursively and translate between
the two forms.
Lesson 26: Percent Rate of Change
● (^) Students develop a general growth/decay rate formula in the context of compound
interest.
● (^) Students compute future values of investments with continually compounding
interest rates.
Lesson 27: Modeling with Exponential Functions
● (^) Students create exponential functions to model real-world situations.
● (^) Students use logarithms to solve equations of the form ft()=×abct for t.
● (^) Students decide which type of model is appropriate by analyzing numerical
or graphical data and verbal descriptions and by comparing different data
representations.
Lesson 28: Newton’s Law of Cooling, Revisited
● (^) Students apply knowledge of exponential and logarithmic functions and
transformations of functions to a contextual situation.
Topic E: Geometric Series and Finance
Topic E is a culminating series of lessons driven by MP.4 (model with mathematics).
Students apply what they have learned about mathematical models and exponential growth
to financial literacy, while developing and practicing the formula for the sum of a finite
geometric series. Lesson 29 develops the future value formula for a structured savings plan
and, in the process, develops the formula for the sum of a finite geometric series (A-SSE.B.4).
The summation symbol, Σ, is introduced in this lesson.
Lesson 30 introduces loans through the context of purchasing a car. To develop the
formula for the present value of an annuity, students combine two formulas for the future
value of the annuity (F-BF.A.1b) and apply the sum of a finite geometric series formula.
Throughout the remaining lessons, various forms of the present value of an annuity formula
are used to calculate monthly payments and loan balances. The comparison of the effects of
various interest rates and repayment schedules requires that students translate between
symbolic and numerical representations of functions (F-IF.C.9). Lesson 31 addresses the issue
of revolving credit such as credit cards, for which the borrower can choose how much of the
debt to pay each cycle. Students again sum a geometric series to develop a formula for this
scenario, and it turns out to be equivalent to the formula used for car loans. Key features of
tables and graphs are used to answer questions about finances (F-IF.C.7e).
Lessons 32 and 33 are modeling lessons in which students apply what they have learned
in earlier lessons to new financial situations (MP.4). Lesson 32 may be extended to an open-
ended project in which students research buying a home and justify its affordability. Lesson
33, the final lesson of the module, is primarily a summative lesson in which students formulate
a plan to have $1 million in assets within a fixed time frame, using the formulas developed in